Chapter 5, Problem 68CR

The accompanying data represent x = Amount of catalyst added to accelerate a chemical reaction and y = Reaction time:

1. a. Calculate the value of the correlation coefficient, r. Does the value of r suggest a strong linear relationship?
2. b. Construct a scatterplot. From the plot, does the word linear provide the most effective description of the relationship between x and y? Explain.

To determine

Find the correlation coefficient.

Explain whether the correlation coefficient suggest a strong relation or not.

Answer to Problem 68CR

The correlation coefficient is –0.981.

Explanation of Solution

Calculation:

The given data relates to the amount of catalyst added in a chemical reaction, x and the reaction time, y. The correlation coefficient is denoted by r.

Correlation coefficient:

Software procedure:

Step by step procedure to obtain the correlation coefficient using the MINITAB software:

• Choose Stat > Basic Statistics > Correlation.
• Enter the columns of x, y under Variables.
• Click OK in all dialogue boxes.

Output obtained using MINITAB is given below:

Thus, from the output, the correlation coefficient is –0.981.

Interpretation:

A value of the correlation coefficient, r closer to 1 or –1 suggests a strong correlation coefficient, whereas a value closer to 0 suggests a weak correlation coefficient.

Here, the correlation coefficient is –0.981, which is very close to –1. Evidently, the negative sign suggests a negative relationship between the variables, so that, higher values of x are associated to lower values of y.

Thus, the relationship between x and y is a very strong negative linear relationship.

To determine

Draw a scatterplot of the data set.

Explain whether it is appropriate to describe the relationship between x and y as linear.

Answer to Problem 68CR

The scatterplot of the data set is as follows:

Explanation of Solution

Calculation:

Scatterplot:

Software procedure:

Step by step procedure to draw the scatterplot using the MINITAB software:

• Choose Graph > Scatterplot > Simple > OK.
• Enter the column of y under Y-variables.
• Enter the column of x under X-variables.
• Click OK in all dialogue boxes.

Thus, the scatterplot is obtained.

Interpretation:

A careful observation of the scatterplot reveals that the points do not exactly fall on a straight line. Rather, the points appear to form a curve with a wide arc.

Hence, it is not appropriate to describe the relationship between x and y as linear.

The arc of the curve being very wide, none of the points would fall to far away from a line drawn through the plot. As a result, the correlation coefficient in Part a has a very high negative value.